Discharge Coefficient Correlations for Circular-Arc Venturi Flowmeters at Critical (Sonic) Flow

Data are presented which tend to verify the theoretically predicted discharge coefficients for circular-arc venturi flow meters operating in the critical flow regime (sonic) at throat Reynolds numbers above 1.5 10⁵. Extensive analysis of the data is presented using methods that are presently in process of international standardization. The data tend to verify the theoretically predicted decrease of 0.25 percent in the discharge coefficient during transition from laminar to a turbulent boundary layer. The transition occurred at a throat Reynolds number of 2.2 10⁶, but the transition point probably changes as a function of several influences. The mean line of the measured data fell between the theoretical values for laminar and turbulent boundary layers. The scatter in 55 data points was ±0.212 percent (95 percent confidence level) from the mean line equation for Reynolds numbers from 4.1 10⁴ to 3.4 10⁶, which included the effects of several variables. Data were obtained from 17 venturis with throat sizes from 0.15 to 1.37 in. with Beta ratios ranging from 0.014 to 0.25. Four different test gases and three primary flow measurement facilities were used. Additional data are presented extending down to throat Reynolds numbers of 1.3 10⁴ and throat diameters of 0.05 in. which indicate special problems in these regions. The state of the art for measuring venturi throat diameters presented a major limitation to the correlation effort. Calibration is necessary in many cases depending on various parameters and requirements. Additional study is needed to determine the optimum geometrical parameters at low Reynolds numbers, the optimum approach configuration for Beta ratios above 0.1, the effect of surface roughness on the discharge coefficient, and the effect of various operational variables such as flow pulsation and approach velocity profile. Also, a continuous effort should be made to improve the critical flow functions for real gases as better gas property data become available, and to extend these calculations to broader ranges of pressures and temperatures, and to other gases.